A festschrift for Herman Rubin by Dasgupta A. (ed.)

By Dasgupta A. (ed.)

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Edu Keywords and phrases: restricted parameter spaces, minimaxity, admissibility, dominating procedures, maximum likelihood estimation. AMS 2000 subject classifications: 62-02, 62C99, 62C15, 62C20, 62C10, 62F10, 62F30. 1 Department 21 22 E. Marchand and W. E. Strawderman the original space) is non-compact. In this case it often happens that these classical estimators are minimax in both the original problem and the restricted problem. If the restriction is to a convex subset, projection of the classical procedure onto the space will typically produce an improved minimax procedure, but the resulting procedure will usually not be admissible because of violation of technical smoothness requirements.

The application of the above results to the strong-admissibility problem is straightforward. 1) is σ-finite. 22) that is ν-symmetric. Therefore the above theory applies to the Markov chain W = (W0 , W1 , W2 , . ) on Θ∞ defined by R(dθ|η). 1” stated in the introductory section of this paper. 4. Suppose the Markov chain W with state space Θ and transition function R(dθ|η) is locally-ν-recurrent. 2) is strongly-admissible. Proof. 7) is zero for each νproper set C. 3 holds. Thus, Q(dθ|x) is strongly admissible.

1961). Estimation with quadratic loss. In Proc. Fourth Berkeley Symp. Math. Statist. Probab. 1, 361–380. Berkeley: University of California Press. MR133191 [15] Johnson, B. (1991). On the admissibility of improper Bayes inferences in fair Bayes decision problems. D. Thesis, University of Minnesota. [16] Johnstone, I. (1984). Admissibility, difference equations and recurrence in estimating a Poisson mean. Ann. Statist. 12, 1173–1198. MR760682 [17] Johnstone, I. (1986). Admissible estimation, Dirichlet principles, and recurp .

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